Self-descriptive sequences
---------------------------
"1C 1O 1N 1W 1A 1Y." That is almost the beginning of "Look and Say", Conway's extraordinary device for generating (self-descriptive) sequences. In 1986, he had the idea of turning descriptors into what they describe. Thus, his sequence 1, 11, 21, 1211... continues indefinitely once we understand that each term describes what it sees immediately to its left: 11 sees "one 1" to its left, 21 sees "two 1s" immediately to its left, and 1211 sees "one 2 and one 1" just before it... This principle proved immensely popular with mathematics enthusiasts. A sequence can begin however we like, but once the first term has been chosen (here, 1), everything follows automatically (see Tangente 191, 2019). Conway also considered a variant in which the digits of the preceding number are grouped before being described. Thus, 2020 gives 2022 ("two 0s, two 2s"), followed by 1032, then 10111213, etc. Fixed points sometimes arise, such as 22 ("two 2s") or 10213223; these are known as autobiographical numbers because they describe themselves.
The RATS conjecture
------------------
